Résondre et disucter le système:
\[
\sum_{a, b}:\left\{\begin{array}{l}
(a+b) x+(a-b) y=2 \\
\left(a^{3}+b^{3}\right) x+\left(a^{3}-b^{3}\right) y=2\left(a^{2}+b^{2}\right)
\end{array}\right.
\]
(déterminant Da,b chc-)

Step 1 ：We are given the system of equations: \[\begin{align*} (a+b) x+(a-b) y &= 2 \\ (a^3+b^3) x+(a^3-b^3) y &= 2(a^2+b^2) \end{align*}\]

Step 2 ：First, we solve the first equation for x: \[x = \frac{-a*y + b*y + 2}{a + b}\]

Step 3 ：Substitute x into the second equation: \[y*(a^3 - b^3) + (a^3 + b^3)*(-a*y + b*y + 2)/(a + b) = 2*a^2 + 2*b^2\]

Step 4 ：Solve the resulting equation for y: \[y = \frac{1}{a - b}\]

Step 5 ：Substitute y back into the first equation to find the solution for x: \[x*(a + b) + 1 = 2\]

Step 6 ：Solve the resulting equation for x: \[x = \frac{1}{a + b}\]

Step 7 ：Final Answer: The solutions to the system of equations are \(\boxed{x = \frac{1}{a + b}}\) and \(\boxed{y = \frac{1}{a - b}}\).